Question

1. |x + 10| = 7 . 2. . |3 + 2x| = 2 - 3x 3. 14 = 7|x + 1| . 4. |2x - 1| = 7 . 5. 2|x - 1| + 1 = 9 . 6. |x| - 11 = 1 .

Answer 1

Ответ:

1.- 3, место Х

2.- 2, место Х

3. 6, место Х

4. 4, место Х

5. 4,5, место Х

6. 12, место Х

Пошаговое объяснение:

1.- 3+10=7

2.3+2×(-2)=2-3×(-2)

Крч и т.д

Answer 2

To solve these absolute value equations, we'll consider both the positive and negative cases for the absolute value expression and solve for x in each case. Here are the solutions for each of the equations:

1. |x + 10| = 7:

   Positive case: x + 10 = 7 x = 7 - 10 x = -3

   Negative case: -(x + 10) = 7 -x - 10 = 7 -x = 7 + 10 -x = 17 x = -17

   So, the solutions are x = -3 and x = -17.

2. |3 + 2x| = 2 - 3x:

   Positive case: 3 + 2x = 2 - 3x 5x = -1 x = -1/5

   Negative case: -(3 + 2x) = 2 - 3x -3 - 2x = 2 - 3x (Note that the absolute value of a negative number is its positive counterpart) -3 = 2 (This case has no solution)

   So, the only solution is x = -1/5.

3. 14 = 7|x + 1|:

   Divide both sides by 7: 2 = |x + 1|

   Positive case: x + 1 = 2 x = 2 - 1 x = 1

   Negative case: -(x + 1) = 2 -x - 1 = 2 -x = 2 + 1 -x = 3 x = -3

   So, the solutions are x = 1 and x = -3.

4. |2x - 1| = 7:

   Positive case: 2x - 1 = 7 2x = 7 + 1 2x = 8 x = 8/2 x = 4

   Negative case: -(2x - 1) = 7 -2x + 1 = 7 -2x = 7 - 1 -2x = 6 x = 6/(-2) x = -3

   So, the solutions are x = 4 and x = -3.

5. 2|x - 1| + 1 = 9:

   2|x - 1| = 9 - 1 2|x - 1| = 8

   Divide both sides by 2: |x - 1| = 4

   Positive case: x - 1 = 4 x = 4 + 1 x = 5

   Negative case: -(x - 1) = 4 -x + 1 = 4 -x = 4 - 1 -x = 3 x = -3

   So, the solutions are x = 5 and x = -3.

6. |x| - 11 = 1:

   |x| = 1 + 11 |x| = 12

   Positive case: x = 12 x = 12

   Negative case: -(x) = 12 -x = 12 x = -12

   So, the solutions are x = 12 and x = -12.